Validation of subjective manual palpation using objective physiological recordings of the cranial rhythmic impulse during osteopathic manipulative intervention

Intermediate (IM) band physiology in skin blood flow exhibits parallels with the primary respiratory mechanism (PRM) or cranial rhythmic impulse (CRI), controversial concepts of osteopathy in the cranial field (OCF). Owing to inconsistent manual palpation results, validity of evidence of PRM/CRI activity has been questionable. We therefore tried to validate manual palpation combining instrumented tracking and algorithmic objectivation of frequencies, amplitudes, and phases. Using a standard OCF intervention, cranial vault hold (CVH), two OCF experts palpated and digitally marked CRI frequencies in 25 healthy adults. Autonomic nervous system (ANS) activity in low frequency (LF) and IM band in photoplethysmographic (PPG) forehead skin recordings was probed with momentary frequency of highest amplitude (MFHA) and wavelet amplitude spectra (WAS) in examiners and participants. Palpation errors and frequency expectation bias during CVH were analyzed for phases of MFHA and CRI. Palpated CRI frequencies (0.05–0.08 Hz) correlated highly with mean MFHA frequencies with 1:1 ratio in 77% of participants (LF-responders; 0.072 Hz) and with 2:1 ratio in 23% of participants (IM-responders; 0.147 Hz). WAS analysis in both groups revealed integer number (harmonic) waves in (very) low and IM bands in > 98% of palpated intervals. Phase analyses in participants and examiners suggested synchronization between MFHA and CRI in a subset of LF-responders. IM band physiology in forehead PPG may offer a sensible physiological correlate of palpated CRI activity. Possible coordination or synchronization effects with additional physiological signals and between examiners and participants should be investigated in future studies.

Technical approaches investigating the physiology underlying the CRI were promising yet inconclusive due to their poor match with palpation 12 . Association of CRI/PRM with TH waves in blood pressure, heart rate, respiration, and skin blood flow have been suggested as physiological correlate for the palpation of the CRI/PRM within all parts of the body. However, palpated CRI rates differed frequently by a factor 2 from rates recorded using technical instrumentation 10 . The CRI/PRM thus remains an enigmatic phenomenon, which poses many open questions.
Hitherto, ANS activity relevant for cardiovascular and respiratory systems has been widely accepted to appear as a low frequency (LF, 0.05-0.15 Hz) and a high frequency (HF, 0.15-0.4 Hz) band. This concept and that of TH waves supposedly accounting for the CRI/PRM have recently been challenged suggesting the CRI/ PRM as a manifestation of '0.15 Hz rhythm band' physiology 13 , also referred to as intermediate (IM) band. Activity in the '0.15 Hz frequency band' has been shown to emerge in various peripheral systems in humans during hypnoid relaxation [14][15][16][17] . These authors had hypothesized that the emergence of the '0.15 Hz rhythm band' in humans corresponds with findings in canine unspecific neurons in the reticular formation of the lower brainstem termed the 'retR' 16,18 . Recent functional magnetic resonance imaging (fMRI) studies suggest IM band fluctuations in humans also originate in the brainstem 19 . Furthermore, IM band activity in heart rate variability (HRV) and respiration was associated with blood oxygen level-dependent (BOLD) activity in an interoceptive processing network 20 . It is of note, that recent suggestions view interoception as a key to a neurological model in osteopathy 21 .
The frequency range of the IM band (0.15 Hz ± 0.03 Hz), the formation of beat oscillations, and integer number phase-synchronization with respiration, HRV, and blood pressure 16 are all well in keeping with currently held notions on explaining the origin of the CRI/PRM. Moreover, upper or lower harmonic waves of IM primary band 17 may well account for reported regular variations in palpated CRI rates, a still puzzling phenomenon of the CRI/PRM 10 . The possibility of lower harmonic waves as a source of rhythmic activity has previously been discussed by osteopathic researchers 11 .
The hypothesis put forth by Pelz 13 has gained further support from current results of our research group. In a larger group a standard OCF treatment, cranial vault hold (CVH), triggered an immediate decline in forehead skin blood oscillations from activity at 0.12 Hz (IM band activity) during control conditions (eyes open, eyes closed) to stable activity in the LF band at 0.07 Hz. These oscillations may represent lower harmonic waves of the primary IM band 22 . A smaller subset of participants remained at primary IM band frequencies. Open questions concern the validation of palpated events with ANS related rhythmic activity in skin blood flow waves. A previous study demonstrated a poor interrater reliability, which put the validity of OMT further into question 23 . Also, the observation that CRI rates palpated by unexperienced examiners were found to be consistently above those palpated by more experienced examiners put the entire concept further into question 24 . Yet another questionable concept concerns the current OMT model used to describe palpated events as 'flexion' and 'extension' events, supposed to account for one complete CRI cycle. However, one CRI cycle does not consistently amount to supposedly complete rates (1:1 ratio) attained by instrumented recordings as higher palpated rates (2:1 ratio) have also been reported 10 .
To resolve these questions concerning the validity of the CRI/PRM concept of OCF, we designed a hardwaresoftware approach, which combined a Bluetooth-equipped footswitch to mark palpated rhythmic activity with semi-linear high temporal resolution algorithms for the analyses of frequency, amplitudes, and phases. This approach should allow to reliably test the validity of ANS physiological activity and concomitant palpated CRI rhythmic activity during CVH, a specific OCF intervention.
Employing these techniques, we tested the following hypotheses: (1) Time intervals palpated at the skull and marked with the footswitch match CRI rates reported in the literature for experienced examiners; (2) Palpated CRI rates are equivalent to autonomic nervous system (ANS) rhythmic activity in photoplethysmographic (PPG) forehead skin recordings in frequencies of IM-band physiology (0.12-0.18 Hz) and their corresponding lower harmonic waves (0.06-0.09 Hz); (3) Wavelet amplitude spectra (WAS) detect primary IM-band and its harmonic waves of lower amplitude responsible for rhythmic activity confounding palpation results; (4) Phasic footswitch responses contain information on palpated CRI ANS related activity which is reflected also by dynamics of momentary frequency of highest amplitude (MFHA); (5) Phases of MFHA correlate with manually palpated 'flexion' and 'extension' .

Participants.
A convenience sample of twenty-five healthy adults (14 female, age 42.4 (± 13.1) years) was recruited by the investigators through word of mouth. Five participants completed two measurements at an interval of 1 week, resulting in a total of 31 measurements. One measurement had to be excluded, as palpation records were faulty. All participants were non-smokers, none had any OMT in the preceding three months. Exclusion criteria were mental health symptomatology, a history of or acute neurological or cardiovascular disorders, current use of psychoactive medication as well as high-performance sport. Furthermore, participants were asked to abstain from caffeine for 4 h and alcohol consumption for 48 h prior to testing. Study design. The study used a double-blind design with examiners as well as participants being naïve to data recording and data analysis performed offline. A between-subjects design was used, however, all participants analyzed in the current manuscript had been allocated to the cranial vault hold (CVH) intervention employed to palpate triggered CRI activity. Performed at comfortable room temperature, experimental sessions consisted of five consecutive sections (initially 300 s, but extended to 330 s after the first measurements to account for artifacts due to section transitions). These additional sections were clipped from all signals prior to analysis. CVH sections were braced by eyes-open (EO) and eyes-closed (EC) sections serving as within-subject control conditions. During CVH eyes were kept closed as well. Thus, the final order was: EO, EC, EC + CVH, EC' , EO' . The two resting state phases were "hands-off " during which the physician's hands had no contact with the participant. The third phase employing CVH was the only "hands-on" phase (see also Fig. 1). As the current investigation focused on physiological correlates of palpation sensations, only the CVH section was analyzed. CVH is a standardized osteopathic hands-on technique which incites defined cranial regions and cranial bones at very low pressure on the scalp. Examiners utilized commonly agreed techniques to execute CVH 25 . Upon recognition of an arriving tide (in OCF commonly denoted as extension) the footswitch was pressed, and upon subsiding of the tide (denoted as flexion) the footswitch was released. Therefore, the interval between two consecutive footswitch operations marks the extension part of the CRI. This procedure is in line with most CRI trials that recorded laser Doppler flowmetry (LDF) data of skin blood perfusion 9 . PPG recordings used a reflective PPG probe placed on the glabella forehead region of participant and examiner. The examiner was seated behind the head of the participant who remained in a supine position.

Instrumentation.
A commercially available footswitch was in-house modified to be able to track palpation sensations of CRI activity using a Bluetooth module. Prior to the recordings used for the study, examiners practiced sufficiently to get acquainted with the use of the footswitch. The PPG device used a standard Osram SFH7060 PG sensor able to emit red, infrared, and green light and simultaneously detect signals using a built-in photodiode. The data from this sensor are further processed with a microcontroller firmware which recorded the reflected red-light signals at 660 nm at a sample rate of 125 Hz since we focused on autonomic nervous system oscillations < 0.4 Hz only (see Fig. 2). The recorded data was synchronized using timestamps. All sensors (participant PPG, examiner PPG, and examiner footswitch) were time-synchronized in the beginning of each measurement with a relative difference of less than 10 ms. The synchronized data stream was transmitted to a local computer using Bluetooth 4.0 protocol, and the entire measurement was uploaded to a private cloud for future offline processing.
Grouping LF-and IM-responders. In a parallel publication 22 we reported on differential physiological responses in LF, IM, and HF activity during CVH computed from PPG data. Submitted to a K-means cluster analysis 26 participants were clustered into different groups based on their physiological responses during CVH. This resulted in one group showing a sudden decline from 0.14 (primary IM band activity) to 0.072 Hz (LF activity), whereas a second group remained in IM mode. The former was therefore referred to as LF-responders, and the latter referred to as IM-responders.

Figure 1. Experimental paradigm.
Each session was comprised of 5 sections, lasting 300/330 seconds each. Section 1 and 5 (eyes open) as well as section 2 and 4 (eyes closed) were performed "hands-off ". Section 3 was "hands-on" during which examiners applied the cranial vault hold (CVH), recording palpation intervals by operating the Bluetooth footswitch. During the entire session, forehead skin blood oscillations (photoplethysmography) were recorded for participant and examiner. Wavelet amplitude spectra. MFHA analysis may discard important physiological information on frequencies of lower amplitude and may thereby account for a misleading display of frequencies. Such frequencies of lower amplitude are of particular relevance in our context since they may represent lower or upper harmonic waves of IM or LF band activity. To gain a better understanding of frequencies of PPG data and palpated extension www.nature.com/scientificreports/ intervals, we used multiple Gaussians to fit the wavelet amplitude spectrum (WAS), since the wavelet response is falling off with the distance to the underlying frequency: where f is the frequency, a is the height of the curve's peak, b is the position of the center of the peak, and c is the width of the curve. Since the number of dominant frequencies may be different at each point in time, we repeated the fit with n = 1 − 6 Gaussians and selected the function which described the WAS best (see Fig. 5) . Several examples of amplitude-frequency distributions were examined, which were considered to be representative for the majority of data.
Phase computations and analyses. In an exploratory analysis, phases of palpated frequencies and MFHA at the time of push (start) and release (stop) of the footswitch were computed for examiners and participants. This was done to exclude a possible 'frequency bias' towards expected frequencies unrelated to palpated frequencies.
Histograms of phases of palpated sections as well as MFHA were computed to examine phase occurrences. Palpation errors (deviation of MFHA and CRI frequency for each palpated interval) were plotted against phases of CRI or MFHA. Furthermore, to probe co-occurrence of phases in CRI and MFHA, scatterplots were created for both parameters for participants as well as examiners. Scatterplots were investigated for certain patterns such as grouping of CRI and MFHA phases at certain phases. Pearson's r correlations were computed for CRI and MFHA phases and independent t-tests compared mean correlation coefficients between participants and examiners in each group (LF-responders, IM-responders).

Frequencies of palpated waves and momentary frequency of highest amplitude. Examiners
palpated 377 extension intervals in LF-responders who responded to CVH (N = 24) with a sudden decline from 0.14 (primary IM band activity) to 0.072 Hz (LF activity), and 124 extension intervals in IM-responders (N = 7) that remained in IM mode during CVH. In a first step of signal analysis, the palpated ' extension' time intervals, calculated extension frequencies, and CRI frequencies computed thereof were superimposed with lowpass filtered (5 Hz) PPG data ( Fig. 3A and B). This showed that palpated extension intervals captured waves in PPG signals at IM band frequencies between 0.12 and 0.16 Hz (≡ 7.2-9.6 cpm; see e.g., recording 'participant A14' in Fig. 3). Dividing extension rates by 2 yielded CRI rates (i.e., a complete cycle of extension and flexion) in the LF band between 0.06 and 0.07 Hz (≡ 3.6-4.2 cpm). Such rates are in agreement with rates reported in the literature for experienced examiners 10,24 . For further visual inspection, MFHA of PPG forehead skin blood flow were superimposed on CRI rates during CVH (see Fig. 4A-D for two representative subjects). The raw PPG data of participant A5 (LF-responder) showed prominent large waves, also known as beat, resonance, or spindle waves at stable low oscillating LF-band activity at 0.07 Hz (Fig. 4A). Superimposing this graph with computed CRI rates exhibited a distinct fit (Fig. 4B). Raw PPG data of participant A14 (IM-responder) ( Fig. 4C and D) showed no beat or spindle waves during CVH. Here, MFHA exhibited unstable IM band activity with two short lived episodes of LF activity and hardly any fit between MFHA and computed CRI activity. Table 1 lists computed mean CRI activity, corresponding MFHA rates, and differences between these (in [Hz]) for the two subsets of participants. For LF-responders, independent t-tests showed a non-significant difference between examiner A and B for mean MFHA (t(21) = 2.0, p = 0.06) and a significant difference for mean palpation frequency (t(21) = 2.1, p = 0.05). However, there was a non-significant difference between examiner A and B for "MFHA-Palpation deviations" (t(21) = 0.7, p = 0.44). In LF-responders, the computed CRI frequencies and MFHA frequencies were at a ratio of 1:1. Here, the absolute numbers of mean MFHA matched the mean of computed absolute CRI frequencies in most cases (M MFHA = 0.071 Hz; M CRI = 0.066 Hz). In IM-responders this ratio was 1:2 since absolute numbers of mean MFHA and the mean of computed absolute CRI rates differed by a factor 2 (M MFHA = 0.147 Hz; M CRI = 0.068 Hz). Correlation analysis of mean MFHA and mean computed CRI frequencies showed high correlations in LF-responders (r = 0.72, p < 0.001) as well as in IM-responders (r = 0.83, p < 0.05). These exploratory correlation analyses encompassed within-and between-subjects variance since 5 of the participants were palpated twice. Nevertheless in a mixed linear model, the association between mean MFHA and mean CRI frequencies remained significant when considering the noise structure (F(1, 13.65) = 35.8, p < 0.001). Furthermore, the effect of different examiners (F(1, 22.2) = 0.98, p = 0.33) as well as the effect of the repeated measure (F(1, 6.3) = 2.2, p = 0.18) did not reach significance.
In Fig. 4D it appears as though palpation misses ANS activity exhibited by MFHA. However, further analyses suggest it may be a matter of detailed information, which was not graphically displayed by MFHA analyses. Figure 5A and B further demonstrate this problem by displaying two examples of different harmonic waves discarded or suppressed by MFHA analysis. Figure 5A (LF-responder) shows a dominant MFHA wave at 0.064 Hz and a smaller wave at 0.15 Hz, representing most likely an upper harmonic of the former, which is yet not displayed by MFHA. The corresponding extension section was palpated at 0.154 Hz. CRI activity computed at 0.075 Hz (≡ 4.5 cpm) was slightly off the actual MFHA at 0.064 Hz. Figure 5B shows an IM-responder with a dominant broad-based MFHA wave at 0.157 Hz and a slightly smaller narrow-based wave at 0.03 Hz (very low frequency (VLF) range), most likely a lower harmonic of the former. This, too, was discarded by MFHA. The corresponding extension section was palpated between the two peaks of MFHA and VLF activity at 0.065 Hz, and CRI activity was computed at 0.035 Hz (≡ 2.09 cpm).
Further, we assessed the presence of upper or lower harmonic waves in wavelet amplitude spectra (WAS). In both LF-responders and IM-responders, harmonic waves were present in 98% of cases in dominating VLF, LF, and IM activity. While frequencies in both examples were widely similar, the mismatch between Fig. 5A and B (1) www.nature.com/scientificreports/ is striking. In the first example (Fig. 5A) palpation captured a smaller IM band wave, and the CRI corresponded with the larger LF wave. In the second example, a large IM band wave was apparently missed by palpation (interval #9) while the CRI corresponded with VLF activity. Quantification of palpated frequency bands showed that 12.1% of all palpations in IM-responders were within the VLF range (below 0.05 Hz) whereas in LF-responders only 3.4% of all palpations were VLF frequencies.
A more precise estimate of deviations of palpations from MFHA was obtained by computing the root mean square of differences between MFHA and CRI ( Fig. 6A-C). There were low deviations in LF-responders and high deviations in IM-responders. The palpation deviation was also highly correlated with LF interval durations (r = − 0.97, p < 0.001). This suggests that a stable strong MFHA frequency in the LF range was related to palpations with low deviation from MFHA, i.e., a relatively exact palpation. However, MFHA fluctuating between the LF, IM and HF range was related to a larger deviation to palpations (Fig. 6B). LF-responders showed relatively small deviations of palpation and MFHA across CVH intervention whereas IM-responders showed an increasing palpation error as experimental time progressed (Fig. 6C).
Analysis of palpation phase. Exploratory analyses of phases of palpated frequencies and MFHA at the time of push (start) and release (stop) of the footswitch were performed to rule out the possibility of 'frequency-or rhythm-bias' , i.e., that examiners could have followed own rhythms or a certain expected rhythm without responding to real palpated sensations (Fig. 7A-F). Distinct peaks for start and stop phases of palpated frequencies and almost identical peaks for the phases of MFHA suggest that palpation occurred not arbitrarily or randomly. Both histograms of LF-responders show peaks at approx. − 140 degrees and 40 degrees for both To determine whether the high correlation of CRI and MFHA phases of participants was arbitrary and would occur at similar probability between CRI and MFHA phases of examiners, scatterplots of CRI and MFHA phases for participants and examiners were computed (see Fig. 8). This showed random distributions in IM-responders for both participants and examiners ( Fig. 8D; participants: r = 0.24; range − 0.1 to 0.6; examiners: r = 0.44; range 0.1 to 0.6). On the other hand, scatterplots of CRI and MFHA phases for LF-responders showed systematic distributions clustering around − 150° and 30° in participants (r = 0.80; range 0.42 to 1.0). In few cases, the negative phase was related to the examiner's start signal and the positive phase to the stop signal, while the opposite was observed in other participants (see also Fig. 7). This also showed that more than half of examiners' scatterplots had less consistent patterns at rather random distributions of CRI and MFHA phases (N = 14, Fig. 8A), more widespread distributions of phases (N = 7, Fig. 8B), or similarly, clustered peaks of phases as were observed in participants (N = 2, Fig. 8C). For LF-responders, the CRI and MFHA phases were significantly less correlated in examiners (r = 0.40; range − 0.2 to 0.93) compared to participants (t(22) = − 2.1, p < 0.05; Fig. 8E).

Discussion
This communication was a first attempt to validate cranial rhythmic impulse (CRI) activity using digitally marked palpation of extension intervals as well as frequency and phase computations of forehead skin perfusion oscillations. Two experienced examiners marked subjective sensations during manual palpation of rhythmic events in the skin of the cranium. Palpations were related to PPG data of forehead skin perfusion. Probing physiological correlates of palpation is of relevance for several reasons. Firstly, palpation of rhythmic activity in humans has a longstanding history in medicine in general. Secondly, palpation is of crucial relevance in the practice of osteopathic manipulative treatment (OMT) 30 . Thirdly, though CRI/PRM has been the subject of numerous studies, the statement of McPartland and Mein 8 still holds today: "The CRI phenomenon is poorly understood, and its functional origin remains unknown, despite its significance in CST (cranial-sacral treatment)".
In a previous study 22 , we identified autonomic nervous system (ANS) activity in the low frequency (LF) and in the intermediate (IM) frequency range in forehead skin perfusion in response to a cranial vault hold (CVH) intervention. We showed that the majority (77%) of participants responded to CVH with highly stable low oscillating activity at 0.07 Hz (LF-responders), while 23% of participants showed seemingly unstable high oscillating IM-band activity at 0.147 Hz (IM-responders). In the current communication, this data set was analyzed with respect to palpations marked by two osteopathic practitioners during CVH. Footswitch-marked palpated extension sections corresponded well with recorded slow PPG waves (Fig. 3). Mean palpated CRI rates (extension interval × 2) at 0.066 Hz for LF-responders and at 0.068 Hz for IM-responders were in line with our www.nature.com/scientificreports/ first hypothesis that observed CRI rates would be comparable with those previously reported for experienced osteopathic practitioners (0.08 Hz; 24 ). Wavelet amplitude spectra revealed ANS related VLF, LF, or IM activity and upper or lower harmonic waves (integer number coupling) in 98% of LF-and IM-responders, yet with differing distributions of amplitudes (see Fig. 5A and B). For example, a dominant wave at 0.07 Hz was accompanied by an upper harmonic wave (1:2) with lower amplitude at approx. 0.15 Hz (see e.g., Fig. 5A). Of note, we observed a high correlation between the mean MFHA frequencies and the mean CRI frequencies in LF-responders and in IM-responders, which confirmed our second hypothesis. Interestingly, there was a stable 1:1 ratio in LF-responders and a stable 1:2 ratio in IM-responders (mean MFHA LF-responders = 0.071 Hz; mean MFHA IM-responders = 0.147 Hz). This difference of objectively recorded and subjectively assessed rhythmic activity in forehead skin perfusion of IM-responders has already been reported in the literature (for a review, see Fig. 1 in 4) for the ratio between low CRI rates and rates of Traube-Hering (TH) waves (range: 0.1-0.15 Hz) (for a review, see Fig. 1 in 4). This historic TH model, however, falls short to explain the physiological backgrounds of the 1:2 ratio. TH or TH-Mayer waves in humans are associated with a narrow frequency range between 0.1 and 0.15 Hz. Furthermore, it is unlikely that these oscillations are of the same etiology as those which have been described by these historic authors. Originally, Mayer waves have been observed at 0.05 Hz in deteriorating preparations of anesthetized spontaneously breathing rabbits 31 . Furthermore, Traube's and later authors' pivotal works used mostly dogs for their experiments, which may have exhibited a mix of rhythms of sympathetic and reticular origin. However, while sympathetic activity is subject of scaling, meaning that the same wave appears at higher frequencies in smaller species 32 , IM or reticular activity has been shown to emerge under comparable conditions at similar frequencies in humans and Table 1. Frequency of CRI activity and momentary frequency of highest amplitude (MFHA) and differences for examiner A and B, and LF-and IM-responders. CRI activity was computed from palpated extension time intervals. Ratios of mean CRI/MFHA for non-responders ranged from 0.38 to 0.55, which yielded an average of 0.46 (approx. 1:2 ratio).  17 . Also, if oscillations recorded by us were of sympathetic origin as those reported for blood pressure, they were to exhibit tonic, that is non-rhythmic qualities 33 . This, however, is not the case since our findings exhibit rhythmically modulated activity. Therefore, we suggest IM band activity to account for 1:2 ratios between palpated CRI and instrumentally recorded MFHA since this model incorporates lower (0.075 Hz) and upper (0.3 Hz) harmonic waves of primary IM frequencies (0.12-0.18 Hz) 17 . This approach has accumulated mounting experimental evidence over the past years 19 and has already been discussed to account for the CRI/PRM 13,20 . Our current findings appear to corroborate this approach further. Our fourth hypothesis of the MFHA in forehead skin rhythms containing information on physiological correlates of CRI palpations is supported by findings on the high overlap of MFHA with palpated CRI rates in LF-responders. This appears as further evidence that the two examiners palpated identical rhythmic sensations at the heads of participants. A possible palpation bias from focusing on anticipated rhythmic events was ruled out by similar CRI and MFHA phases in participants (see Fig. 7A-F). In summary, these findings support the validity of palpated CRI rates by MFHA rates in LF-responders.
Comparing phases of footswitch start and stop signals during palpation of CRI activity with phases of MFHA in participants, revealed a linear 1:1 ratio in a group of 14 LF-responders. However, a random distribution of start and stop phases of CRI and MFHA in examiners suggest that there was no phase synchronization between participants and examiners (Fig. 8A). A smaller group of LF-responders (N = 7, Fig. 8B) showed a 1:1 ratio of    34 . In the corresponding examiners, the synchronization of start and stop of phases of CRI and MFHA was comparable. Whether there is bidirectional triggering of coordination (reversed order of start and stop phases suggests this may be the case) or phase synchronization between examiners and participants cannot be inferred from the current analyses. It is, however, of high relevance and should be probed employing synchrograms and coordigrams 35 . Similarly, a reversal of respiratory sinusarrhythmia has previously been associated with high or moderate levels of fMRI-related anxiety 36 . Correlations between mean phases of MFHA and CRI were significantly higher in participants compared to examiners suggesting successfully triggered CVH effects. In IM-responders, however, CRI and MFHA phases showed only low correlations in participants and in examiners. This suggests there was only poor synchronization in and between participants and examiners.  www.nature.com/scientificreports/ Origin of the 1:2 ratio between CRI and MFHA in IM-responders. The difference of CRI-MFHA ratios between LF-responders and IM-responders may result from the MFHA analysis. As the MFHA solely displays the frequency of highest amplitude, it discards other important frequencies of lower amplitude. Our wavelet amplitude spectra (WAS) further exemplified this shortcoming, as the presence of additional frequencies of lower amplitude could be demonstrated (see Fig. 5A-D). Therefore, our terms LF-responders and IM-responders relate only to MFHA results and should be viewed with caution in the context of palpation. WAS analyses suggest that the palpation frequency in IM-responders relates to lower amplitude harmonic waves. This is in keeping with our two examiners reporting no differences in palpation sensations between LF-responders and IM-responders. Interestingly, three of five participants that were measured twice were both LF-and IM-responders. On the one hand, MFHA differences between consecutive measurements could be suggestive of different physiological reactions. On the other hand, a 2:1 ratio of MFHA and CRI as well as similar palpation frequencies indicates similar reactions and a possible shortcoming of the MFHA analysis as lower palpable PPG oscillations were only discovered in the WAS. IM-band activity appears to be a plausible explanation for the origin of the CRI and the PRM, respectively, since inclusion of lower and upper harmonic waves broaden its primary frequency range (0.15 Hz ± 0.03 Hz) exponentially. Associated with this feature is phase-synchronization at 1:1 or 1:2 integer number ratios with respiration, HRV, and blood pressure 17 . This might become a source of confounding as frequencies in interacting subjects synchronize and rhythmic differences 'palpably' dissolve during phase synchronizations. This notion is supported by our findings in a smaller group of LF-responders on highly synchronized phases of CRI and MFHA in both participants and examiners (see Fig. 8B). This, however, mandates further comprehensive data recording and data analyses of synchronization and coordination including at least one additional peripheral system. Flexion and extension: fact or fancy. Flexion and extension refer to palpation sensations in trained observers 7,10 . These terms relate to physiological correlates such as minute scalp motion strong enough to be palpated by sufficiently trained therapists 12 . Osteopaths commonly describe extension as movement towards the examiner and flexion as a movement away from the examiner. In our investigation we marked extension phases to compute the complete CRI. This supplied results which apparently support the construct of flexion and extension given our results for MFHA and WAS. However, based on our data we cannot relate phases of forehead skin MFHA to manually palpated extension and flexion, whereas extension (and flexion) was well distinguishable by examiners. Therefore, a rising or falling edge of the PPG wave is obviously not permanently related to their palpated sensations.
Limitations. The large variation in physiological rhythms 37 as well as in CRI rates 11,38 is a general complication of osteopathic research. The small sample size, the small number of examiners as well as the inclusion of five participants measured on two occasions limit the generalizability of our results. Furthermore, recording and analyses of PPG signals as the only physiological system is prone to leave important physiological questions unanswered.
Outlook. Osteopathy in the cranial field has often been criticized for its contradictory findings. This concerns foremost the limited interrater reliability since experienced and beginning osteopaths showed findings differing by a factor two. By showing overlapping variability of MFHA, WAS, palpation frequencies, and phases during CVH, our analyses offer a first glimpse into resolving the CRI's problematic interrater reliability. However, in our data (Fig. 8C) the interaction of participant and examiner may bear potential to induce significant systemic physiological changes. Factors determining these interactions should be considered in further investigations. Furthermore, we defined two groups of participants responding to CVH in physiologically different modes. Further studies will show whether responses to CVH are related to behavioral parameters and to treatment outcome in general. This will be of importance when investigating CRI and MFHA in patients.

Data availability
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.